Taylor poured rice into Cesar's pryamid to measure it's capacity.
We wrapped up our last unit of math this week with a look at the volume of cones and pyramids using models. The children learned that it takes three cones full of rice to fill a cylinder with the same base and height and it takes three pyramids full of rice to fill a similar prism, thus they know they can find the volume of prisms and cones by first finding the volume of the related shape, then dividing by three. We also learned how to find the surface area of prisms and cylinders using cereal boxes and soup cans. The children have taken in a great deal of new information on measurement and we will spend two days reviewing before they take the unit test next week. You can help your child by talking about the differences between linear, square and cubic measures! Point out whenever you are measuring something and talk about whether you are measuring for volume or capacity. The more real life examples they can experience, the better they will understand these concepts!
May 23, 2008
Chris and Cesar build polyhedra models.
This week we reviewed the properties of solids and consolidated a great deal of vocabulary the children have learned. The children built models of cylinders, cones, prisms and pyramids, then used their models to compare and contrast the properties of these shapes.We also built on previous knowledge of volumes of prisms to help in understanding how to find the volume of cylinders. Today the students measured empty cans and used their measurements to find the volume of the can. They then checked their answers by filling the can with water and checking to see that the liquid capacity matched their calculated volume. It was a wet, but wonderful day! The class also completed another extended response in problem solving and I am very pleased to say that over
Sarah and Joey use the models.
half of the class is now solving these problems and writing complete and well-supported explanations for how they did so. The few children who were not able to solve the problem accurately did choose and use appropriate strategies, but made errors in their computation. This is a big improvement from the beginning of the year when almost a third of the class could not even begin to choose a strategy or write a coherent explanation of their process!
Emil and Daniel measure the radius and height of a can.
Children used water to check the capacity of ther cans.
Students played 3-D Shape sort.
May 10, 2008
This week in math was a challenging one! While it easy to teach a child to memorize the formulas for area and circumference of a circle, it is not as easy to help them understand why those formulas work or what that Greek number pi really is. To help them begin to develop these concepts, students measured the circumference and diameter of round objects, and then divided to find the ratio. By comparing the results of all students, the children came to see that pi is a constant-the ratio of diameter to circumference. We also measured diameter and area, and then looked for a ration between the area and the radius squared. Once again, results were consistently close to pi. The children have had a little practice using the formulas as well and we will continue to practice next week. This is a very abstract concept for most children this age and we do not expect children to fully understand it at this point. If your child seems a little “wobbly” with these formulas, that’s as normal as the wobbly way they walked when they were taking their first steps! Don’t worry-they’ll get plenty of opportunity to get better over the next few years.
Sarah and YuJin measure circumference.
March 7, 2008
Emil works through a page of addition problems.
On Monday students got the results of the Unit 7 test and I pleased to say that the class did very well with this unit. We then launched into Unit 8: Fractions & Ratios. The first few lessons of this unit are a review of addition and subtraction with fractions and mixed numbers. Though there were several workbook pages to review with each lesson, we were able to move through them quite quickly. The children spent the rest of the class time to learn two new games that will help them practice and develop their fraction skills: Mixed Number Spin and Fraction Action, Fraction Friction. Finally, the children worked on their 3rd Krypto challenge and, once again, came up with solutions that were fantastic! In over ten years of teaching Krypto, I have never had such complex solutions at this stage!
Mrs. Hempel checks Daniel's fraction work.
Chelsea and YuJin play Mixed Number Spin.
February 29, 2008
The children practiced adding and subtracting positive and negative numbers through worksheets and games such as Top-It and The Credit-Debit Game this week. The children were also introduced to negative numbers in a four-quadrant grid and practiced plotting coordinate pairs that included integers. Following a day of review yesterday, students completed the test for Unit 7: Exponents and Negative Numbers today. We revisited the problem solving strategy of Using Logical Reasoning through a game called Save the Wumpus, in which children must use deductive reasoning to solve a challenging puzzle. The children loved this game and are now beginning to understand that the strategy of Using Logical Reasoning involves eliminating possibilities in order to find the only possible solution. We also completed out second week of Krypto this week. In Krypto, children practice their mental fact skills and the use of order of operations in an open-ended problem solving situation; they are given five numbers and a target number and they must try to write an equation using all five numbers that equals the target. They must use each number exactly one and they can use any operation. They are also allowed to use exponents, square roots, summations and factorials to solve the problem. It is impressive to see the number of amazing solutions they find! This week’s numbers were 2,3,4,5 and 8, and the target was 100. Below is a picture of this week’s solutions!
This week's Krypto solutions!
February 22, 2008
This week in math the children were introduced to the very difficult skills of adding and subtracting positive and negative numbers. After some work with manipulatives, and with a little help, the class was able to generate a set of rules for adding and subtracting integers. After a little practice with these new skills, the children practiced through two new games; Integer Top It and The Credit/Debt Game. Because this is a new skill, many of the students were feeling somewhat insecure about it at the end of the week. If your child was one of those who was worried, please reassure them that we will continue to practice with integers next week!
Students use slates to practice adding integers.
Logan challenges Chelsea to a game of Integer Top It
January 18, 2008
We spent a good deal of our math time this week learning how to find common denominators and adding and subtracting fractions. The class learned a new game called Fraction Capture, which was a huge hit, and they reviewed several basic fraction skills, such as converting mixed numbers to improper fractions or fractions to decimals and percents. We also took time to analyze a data organization activity and the children used that to reflect on what they have learned and what they still need to practice with landmark numbers and simple data sets. Finally, we continued to work on our problem solving booklet. Two important ideas were introduced this week: good problem solving know that there is usually more than one way to solve a problem, and good problem solvers switch strategies when the method they are trying isn’t working!
Fractin Capture is full of surprises!
January 11, 2008
We started a new unit this week that will review and build on previous learning about using and organizing data, and the use of fractions and decimals and percents, and introduce some basic concepts of probability. This week the children how to generate a stem-an-leaf plot from a set of survey data and how to find landmarks such as maximum, minimum, median and node from their plots. They also explored the concept of data sampling and the relationship between sample size and the reliability of predictions you can make from a sample. Also, we started to play a game called First to 21 and to record the numbers of wins and loses for each player. Next week we will use this data to analyze whether or not this is a fair game.
Another new routine that was introduced this week was Problem Solver activities. Each student received a booklet of word problems and each week I will introduce and/or review a few problem solving strategies. We will discuss how to recognize when to use each strategy and how to apply it in different problem solving situations. The children will then practice by completeing the problems in their packets.
May 30, 2008
May 23, 2008
May 10, 2008
This week in math was a challenging one! While it easy to teach a child to memorize the formulas for area and circumference of a circle, it is not as easy to help them understand why those formulas work or what that Greek number pi really is. To help them begin to develop these concepts, students measured the circumference and diameter of round objects, and then divided to find the ratio. By comparing the results of all students, the children came to see that pi is a constant-the ratio of diameter to circumference. We also measured diameter and area, and then looked for a ration between the area and the radius squared. Once again, results were consistently close to pi. The children have had a little practice using the formulas as well and we will continue to practice next week. This is a very abstract concept for most children this age and we do not expect children to fully understand it at this point. If your child seems a little “wobbly” with these formulas, that’s as normal as the wobbly way they walked when they were taking their first steps! Don’t worry-they’ll get plenty of opportunity to get better over the next few years.
March 7, 2008
On Monday students got the results of the Unit 7 test and I pleased to say that the class did very well with this unit. We then launched into Unit 8: Fractions & Ratios. The first few lessons of this unit are a review of addition and subtraction with fractions and mixed numbers. Though there were several workbook pages to review with each lesson, we were able to move through them quite quickly. The children spent the rest of the class time to learn two new games that will help them practice and develop their fraction skills: Mixed Number Spin and Fraction Action, Fraction Friction. Finally, the children worked on their 3rd Krypto challenge and, once again, came up with solutions that were fantastic! In over ten years of teaching Krypto, I have never had such complex solutions at this stage!
February 29, 2008
The children practiced adding and subtracting positive and negative numbers through worksheets and games such as Top-It and The Credit-Debit Game this week. The children were also introduced to negative numbers in a four-quadrant grid and practiced plotting coordinate pairs that included integers. Following a day of review yesterday, students completed the test for Unit 7: Exponents and Negative Numbers today. We revisited the problem solving strategy of Using Logical Reasoning through a game called Save the Wumpus, in which children must use deductive reasoning to solve a challenging puzzle. The children loved this game and are now beginning to understand that the strategy of Using Logical Reasoning involves eliminating possibilities in order to find the only possible solution. We also completed out second week of Krypto this week. In Krypto, children practice their mental fact skills and the use of order of operations in an open-ended problem solving situation; they are given five numbers and a target number and they must try to write an equation using all five numbers that equals the target. They must use each number exactly one and they can use any operation. They are also allowed to use exponents, square roots, summations and factorials to solve the problem. It is impressive to see the number of amazing solutions they find! This week’s numbers were 2,3,4,5 and 8, and the target was 100. Below is a picture of this week’s solutions!
February 22, 2008
This week in math the children were introduced to the very difficult skills of adding and subtracting positive and negative numbers. After some work with manipulatives, and with a little help, the class was able to generate a set of rules for adding and subtracting integers. After a little practice with these new skills, the children practiced through two new games; Integer Top It and The Credit/Debt Game. Because this is a new skill, many of the students were feeling somewhat insecure about it at the end of the week. If your child was one of those who was worried, please reassure them that we will continue to practice with integers next week!
January 18, 2008
We spent a good deal of our math time this week learning how to find common denominators and adding and subtracting fractions. The class learned a new game called Fraction Capture, which was a huge hit, and they reviewed several basic fraction skills, such as converting mixed numbers to improper fractions or fractions to decimals and percents. We also took time to analyze a data organization activity and the children used that to reflect on what they have learned and what they still need to practice with landmark numbers and simple data sets. Finally, we continued to work on our problem solving booklet. Two important ideas were introduced this week: good problem solving know that there is usually more than one way to solve a problem, and good problem solvers switch strategies when the method they are trying isn’t working!
January 11, 2008
We started a new unit this week that will review and build on previous learning about using and organizing data, and the use of fractions and decimals and percents, and introduce some basic concepts of probability. This week the children how to generate a stem-an-leaf plot from a set of survey data and how to find landmarks such as maximum, minimum, median and node from their plots. They also explored the concept of data sampling and the relationship between sample size and the reliability of predictions you can make from a sample. Also, we started to play a game called First to 21 and to record the numbers of wins and loses for each player. Next week we will use this data to analyze whether or not this is a fair game.
Another new routine that was introduced this week was Problem Solver activities. Each student received a booklet of word problems and each week I will introduce and/or review a few problem solving strategies. We will discuss how to recognize when to use each strategy and how to apply it in different problem solving situations. The children will then practice by completeing the problems in their packets.